This invention relates to a sine wave multiplication circuit and a sine wave multiplication method for multiplying a certain analog signal by a sine wave signal, and more particularly to an analog sine wave multiplication circuit and an analog sine wave multiplication method for a sine wave signal.
It is one of the most basic functions in various signal processes to multiply a certain signal by a sine wave. For example, in frequency conversion of shifting a certain signal by a desired frequency, a sine wave multiplication circuit is required. Further, a sine wave multiplication circuit is required essentially also for conversion of a frequency band of a signal into a frequency band in the proximity of zero (direct current) in frequency in order to detect an arbitrary frequency component of the signal.
Here, for example, taking arithmetic operation for determination of an accurate sum of two sine waves as an example, arithmetic operation ofej(ω1t+θ1)·ej(ω2t+θ2)=ej{(ω1+ω2)t+θ1+θ2}  (1)is examined.
Actually, in order to determine the real part of the expression (1) above, arithmetic operation given by the following expression (2) should be performed:Cos(ω1t+θ1)·Cos(ω2t+θ2)−Sin(ω1t+θ1)·Sin(ω2t+θ2)=Cos{(ω1+ω2)t+θ1+θ2}  (2)
The expression (2) above can be implemented, for example, by two analog multiplication circuits. The multiplication circuit used here is called Gilbert multiplier and is disclosed in BARRIE GILBERT, “A Precise Four-Quadrant Multiplier with Subnanosecond Response”, IEEE JOURNAL OF SOLID-STATE CIRCUITS, Vol. SC-3, No. 4, December 1968, pp. 365-373 (hereinafter referred to as Non-Patent Document 1). A circuit configuration of the Gilbert multiplier is shown in FIG. 23.
However, a high degree of accuracy in arithmetic operation cannot be anticipated with such an analog multiplier as described above. The most serious problem is an offset. Transistors of the Gilbert multiplier of FIG. 23 involve mismatching in characteristic. As a result, an offset voltage is superposed equivalently on each of four input signals to the Gilbert multiplier of FIG. 23. As a result, a feed-through phenomenon that the components appear as they are on the output occurs. Further, if the two multiplication circuits 101 and 102 have mismatching in gain, then not only a component of the sum of frequencies ω1 and ω2 but also another component of the difference between the frequencies ω1 and ω2, that is, an image component, appear on the output.
The components can be described in connection with a signal spectrum illustrated in FIGS. 24A and 24B. The output (b) with regard to signals ω1 and ω2 of the input (a) exhibits, in addition to a desired signal of the signal ω1+ω2, feed-through values of the input signals ω1 and ω2 themselves and an image component of the signal ω1−ω2. This is caused by offset voltages of the analog multiplication circuits and a gain error between the two multiplication circuits 101 and 102.
The feed-through matters particularly. The Gilbert multiplier shown in FIG. 23 has such a narrow dynamic range of an input thereto that, in order to use the Gilbert multiplier in a linear region, only a signal of an amplitude of approximately 10 to 20 m Vp−p can be inputted. In contrast, the offset voltage of transistors usually is approximately 1 mV. Accordingly, the feed-through can be suppressed only by approximately −20 dB of the desired signal. In order to further reduce the feed-through, special measures (for example, trimming) in layout or circuit design are required. Even though, it is considerably difficult to assure −40 dB.